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Erschienen in:
Continuum Modeling of Biological Network Formation Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

A Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior

verfasst von : José A. Carrillo, Young-Pil Choi, Sergio P. Perez

Erschienen in: Active Particles, Volume 1

Verlag: Springer International Publishing

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Abstract

This survey summarizes and illustrates the main qualitative properties of hydrodynamics models for collective behavior. These models include a velocity consensus term together with attractive–repulsive potentials leading to non-trivial flock profiles. The connection between the underlying particle systems and the swarming hydrodynamic equations is performed through kinetic theory modeling arguments. We focus on Lagrangian schemes for the hydrodynamic systems showing the different qualitative behaviors of the systems and its capability of keeping properties of the original particle models. We illustrate the known results concerning large-time profiles and blowup in finite time of the hydrodynamic systems to validate the numerical scheme. We finally explore the unknown situations making use of the numerical scheme showcasing a number of conjectures based on the numerical results.

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Vorheriges Kapitel A Kinetic Theory Approach to the Modeling of Complex Living Systems
Nächstes Kapitel Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants
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Metadaten
Titel
A Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior
verfasst von
José A. Carrillo
Young-Pil Choi
Sergio P. Perez
Copyright-Jahr
2017
Buch
Active Particles, Volume 1

Print ISBN: 978-3-319-49994-9

Electronic ISBN: 978-3-319-49996-3

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-49996-3_7

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